%0 Journal Article
%T 调和映照的双Lipschitz性质<br>Bi-Lipschitz Properties for Harmonic Mappings
%A 朱剑峰
%J 数学年刊（A辑）
%D 2018
%R 10.16205/j.cnki.cama.2018.0004
%X 设$w(z)$为单位圆盘$\mathbf{U}$到约当区域$\Omega\subseteq \mathbf{C}$上的 调和映照. 给出$w(z)$具有Lipschitz性质的等价条件. 进一步地, 若$\Omega$为有界凸区域, 对其边界函数给出一个较弱的条件, 使得$w=P[f](z)$为调和拟共形映照.<br>Suppose that $w(z)$ is a harmonic mapping of the unit disk $\mathbf{U}$ onto a Jordan domain $\Omega\subseteq \mathbf{C}$. The author finds some equivalent conditions for the Lipschitz property of $w(z)$. Moreover, if $\Omega$ is a bounded convex domain, a weaker condition on the boundary function $f$ is found, such that $w(z)=P[f](z)$ is a harmonic quasiconformal mapping.
%K 调和映照
%K 调和拟共形映照
%K 双Lipshcitz条件
%K $H^p$空间
%K $h^p$空间&lt
%K br&gt
%K Harmonic mappings
%K Harmonic quasiconformal mappings
%K Bi-Lipschitz condition
%K $H^p$ space
%K $h^p$ space
%U http://www.camath.fudan.edu.cn/camacn/ch/reader/view_abstract.aspx?file_no=39A104&flag=1